Energy considerations in LC oscillations. How is it in SHM?

[weirdo]

Homework Statement

Hi

When you set up an LC (tank) circuit there is oscillation due to charge and discharge of capactor and storage of energy in the inductor.

How do you prove that it is simple harmonic? And also how do you prove (mathematically) energy is conserved in an undamped LC oscillation?

Homework Equations

For C: emf= q/c
For L: emf= -L (dI/dt)

The Attempt at a Solution

emf across C=emf across L
ie, q/c + L (dI/dt) = 0

 

[LennoxLewis]

By setting up an equation of the voltage, using the relevant formulas you've already given, you come to a second order differential equation that, outside of different constants, is equivalent to the second order DE of the harmonic oscillator.

 

[weirdo]

Fine thanks. I got the bit on proving it to be in SHM. How should I start to prove that total energy is conserved in a mathematical way?

I can say let at t=0s, energy of system in in C, E= 1/2 CV² -->1
after 1/4 the time period, energy is fully in inductor, E= 1/2 LI² --> 2

So E_total = 1 + 2.

How do I show it is constant for undamped oscillations?